Re: [Help-glpk] sensitivity analysis

[Andrew Makhorin]

> I read again the documentation. The Chapter 4 helped me a lot. But I
> still do not understand the sensitivity analysis exactly.
> Let see again the the problem:
>  
> max
> 9x1+20x2+45x3
> subject to
> c1:2x1+5x2+15x3<=5000
> c2:4x1+6x2+8x3<=20000
> end
>  
> For the second constraint I get an activity range (6 000;10 000). The
> documentation says:
> "For every auxiliary (row) or structural (column) non-basic variable
> the routine starts changing its active bound in both direction. The
> first of the two lines in the report corresponds to decreasing, and
> the second line corresponds to increasing of the active bound. Since
> the variable being analyzed is non-basic, its activity, which is equal
> to its active bound, also starts changing."
> What is the active bound for the second constraint?
> For me an activity range (+inf;10 000) would be logical. The RHS of
> c2:4x1+6x2+8x3<=20000
> can be increased by any number (because the slack will be higher and
> nothing else happens) and can be reduced by 10 000, ie the constraint
> become
> c2:4x1+6x2+8x3<=10000
> and the second  auxiliary variable become non-basic variable.
>  
> Could you write in one or two sentences how what does (6 000;10 000)
> activity range means for second constraints?

Since row c2 is non-active, that is, its auxiliary variable is basic,
the objective coefficient sensitivity analysis is performed, i.e. what
happens if the objective coefficient at c2 (which initially is 0,
because c2 is an auxiliary variable) starts changing in both direction.
In the analysis report "Obj.coef. range" shows minimal and maximal
values of the objective coefficient at that basic variable on which the
basis is still not changed, and "Activity range" shows corresponding
values of the basic variable if its objective coefficient would have
that value. In your example, if c2 would have obj. coef. -.625, its
value in the optimal basis would be 6000, and if the obj. coef. would
unlimitedly increase, value of c2 would be 10000 (which is its upper
bound). Note that the analysis for basic variables has more sense for
structural variables (columns) rather than for auxiliary ones (rows).